 13–15


BO
 Perform oneoperation computation with whole numbers and decimals
Solve problems in one or two steps using whole numbers
Perform common conversions (e.g., inches to feet or hours to minutes)
 3.NS.2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division
6.AF.2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

PS
 Calculate the average of a list of positive whole numbers
Perform a single computation using information from a table or chart

No explicit CA standard for average.
4.SP.1.3 Interpret oneand twovariable data graphs to answer questions about a situation.
5.SP.1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ.

NS
 Recognize equivalent fractions and fractions in lowest terms
 No explicit CA standard for equivalent fractions.
4.NS.1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions.
5.NS.1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

EE
 Exhibit knowledge of basic expressions (e.g., identify an expression for a total as b+g )
Solve equations in the form x+a=b , where a and b are whole numbers or decimals
 7.AF.1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
3.AF.1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.
3.AF.1.2 Solve problems involving numeric equations or inequalities.

GR
 Identify the location of a point with a positive coordinate on the number line
 4.NS.1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
5.NS.1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

PF



ME
 Estimate or calculate the length of a line segment based on other lengths given on a geometric figure
 4.MG.2.0 Students use twodimensional coordinate grids to represent points and graph lines and simple figures
4.MG.2.2 Understand that the length of a horizontal line segment equals the difference of the x coordinates.
4.MG.2.3 Understand that the length of a vertical line segment equals the difference of the y coordinates.

FU



 16–19


BO
 Solve routine onestep arithmetic problems (using whole numbers, fractions, and decimals) such as single step percent
Solve some routine twostep arithmetic problems
 7.NS.1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

PS
 Calculate the average of a list of numbers
Calculate the average, given the number of data values and the sum of the data values
Read tables and graphs
Perform computations on data from tables and graphs
Use the relationship between the probability of an event and the probability of its complement

No explicit CA standard for average.
4.SP.1.3 Interpret oneand twovariable data graphs to answer questions about a situation.
5.SP.1.2 Organize and display singlevariable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.
5.SP.1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph.
6.SP.3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
6.SP.3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1P is the probability of that event not occurring.

NS
 Recognize onedigit factors of a number
Identify a digit’s place value
 3.NS.1.3 Identify the place value for each digit in numbers to 10,000
4.NS.1.2 Order and compare whole numbers and decimals to two decimal places.

EE
 Substitute whole numbers for unknown quantities to evaluate expressions
Solve onestep equations having integer or decimal answers
Combine like terms (e.g., 2x+5 )
 6.AF.1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
6.AF.1.1 Write and solve onestep linear equations in one variable.
Expression "like terms" not used in CA standards.
1AL1.4 Simplify expressions involving variables by combining like terms (e.g. 5 + 4x  7xy^2 + y^3  2 + 6xy^2 + x^2 y = 3 + 4x  xy^2 + x^2 y + y^3 ).

GR
 Locate points on the number line and in the first quadrant
 4.NS.1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
4.NS.1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").
4.NS.1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

PF
 Exhibit some knowledge of the angles associated with parallel lines
 4.MG.3.1 Identify lines that are parallel and perpendicular.
5.MG.2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools.

ME

Compute the perimeter of polygons when all side lengths are given
Compute the area of rectangles when whole number dimensions are given

3.MG.1.3 Find the perimeter of a polygon with integer sides. 4.MG.1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

FU



 20–23


BO
 Solve routine twostep or threestep arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average
 7.AF.4.1 Solve twostep linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
7.AF.4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

PS
 Calculate the missing data value, given the average and all data values but one
Translate from one representation of data to another (e.g., a bar graph to a circle graph)
Determine the probability of a simple event
Exhibit knowledge of simple counting techniques
 No explicit CA standard.
4.SP.2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
4.SP.2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; \frac{3}{4} ).

NS
 Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor
 4.NS.1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
5.NS.1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.
4.NS.1.2 Order and compare whole numbers and decimals to two decimal places.
7.NS.2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
5.NS.1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3 ).
37MR.1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

EE
 Evaluate algebraic expressions by substituting integers for unknown quantities
Add and subtract simple algebraic expressions
Solve routine firstdegree equations
Perform straightforward wordtosymbol translations?
Multiply two binomials
 5.AF.1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid.
5.AF.1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution
7.AF.4.0 Students solve simple linear equations and inequalities over the rational numbers:
Seems like this should be covered in 6th or 7th grade …
1AL4.1 Add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. (CA.1AL.10)

GR
 Locate points in the coordinate plane
Comprehend the concept of length on the number line
Exhibit knowledge of slope*
 5.AF.1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.

PF
 Find the measure of an angle using properties of parallel lines
Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)
 GE7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
5.MG.2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.
6.MG.2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

ME
 Compute the area and perimeter of triangles and rectangles in simple problems
Use geometric formulas when all necessary information is given
 5.MG.1.0 Students understand and compute the volumes and areas of simple objects:

FU
 Evaluate quadratic functions, expressed in function notation, at integer values


 24–27


BO
 Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)


PS
 Calculate the average, given the frequency counts of all the data values
Manipulate data from tables and graphs
Compute straightforward probabilities for common situations
Use Venn diagrams in counting
 No CA standard uses 'frequency' until PS.8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stemandleaf displays, scatterplots, and boxandwhisker plots.
6.SP.3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).

NS
 Find and use the least common multiple
Order fractions
Work with numerical factors
Work with scientific notation
Work with squares and square roots of numbers
Work problems involving positive integer exponents
Work with cubes and cube roots of numbers
Determine when an expression is undefined
Exhibit some knowledge of the complex numbers †
 6.NS.2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
6.NS.1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
7.NS.1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
7.NS.2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
7.AF.2.1 Interpret positive wholenumber powers as repeated multiplication and negative wholenumber powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
7.AF.2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
7.MG.2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a threedimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.
No CA standard mentions cube roots.
No CA standard mentions undefined expressions.
Complex numbers are first discussed in AL2 5.6 & 8

EE
 Solve realworld problems using firstdegree equations
Write expressions, equations, or inequalities with a single variable for common prealgebra settings (e.g., rate and distance problems and problems that can be solved by using proportions)
Identify solutions to simple quadratic equations
Add, subtract, and multiply polynomials
Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)
Solve firstdegree inequalities that do not require reversing the inequality sign
 1AL2.4 Solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. (CA.1AL.5)

GR
 Identify the graph of a linear inequality on the number line
Determine the slope of a line from points or equations
Match linear graphs with their equations
Find the midpoint of a line segment *
 7.AF.1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
7.AF.1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
1AL 2.5 Understand slope as a constant ratio and are able to derive linear equations by using the pointslope formula. (CA.1AL.7)
1AL 2.3 Can verify that a point lies on a line, given an equation of the line. (CA.1AL.7)
GE.17 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.

PF
 Use several angle properties to find an unknown angle measure
Recognize Pythagorean triples
Use properties of isosceles triangles


ME
 Compute the area of triangles and rectangles when one or more additional simple steps are required
Compute the area and circumference of circles after identifying necessary information
Compute the perimeter of simple composite geometric figures with unknown side lengths


FU
 Evaluate polynomial functions, expressed in function notation, at integer values
Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths


 28–32


BO
 Solve word problems containing several rates, proportions, or percentages


PS
 Calculate or use a weighted average
Interpret and use information from figures, tables, and graphs
Apply counting techniques
Compute a probability when the event and/or sample space are not given or obvious

Definitions:
The weighted mean, or weighted average, of a nonempty list of data [x_1 ,x_2 ,...,x_N ] with corresponding nonnegative weights [w_1 ,w_2 ,...,w_N ] at least one of which is positive, is the quantity calculated by \bar x = \frac{{\sum\nolimits_{i  1}^N {w_i \cdot x_i } }}{{\sum\nolimits_{i  1}^N {w_i } }} = \frac{{w_1 \cdot x_1 + w_2 \cdot x_2 + ... + w_N \cdot x_N }}{{w_1 + w_2 + ... + w_N }}

NS
 Apply number properties involving prime factorization
Apply number properties involving even/odd numbers and factors/multiples
Apply number properties involving positive/negative numbers
Apply rules of exponents
Multiply two complex numbers


EE
 Manipulate expressions and equations
Write expressions, equations, and inequalities for common algebra settings
Solve linear inequalities that require reversing the inequality sign
Solve absolute value equations
Solve quadratic equations
Find solutions to systems of linear equations
 1AL 2.2 Are able to sketch the region defined by linear inequality (e.g. 2x+6y<4 ). (CA.1AL.6)

GR
 Interpret and use information from graphs in the coordinate plane
Match number line graphs with solution sets of linear inequalities
Use the distance formula
Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point
Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)†


PF
 Apply properties of 30°60°90°, 45°45°90°, similar, and congruent triangles
Use the Pythagorean theorem


ME
 Use relationships involving area, perimeter, and volume of geometric figures to compute another measure


FU
 Evaluate composite functions at integer values
Apply basic trigonometric ratios to solve righttriangle problems


 33–36


BO
 Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts from prealgebra and/or pregeometry (e.g., comparing percentages or averages, using several ratios, and finding ratios in geometry settings)


PS
 Distinguish between mean, median, and mode for a list of numbers
Analyze and draw conclusions based on information from figures, tables, and graphs
Exhibit knowledge of conditional and joint probability

5.SP.1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ.
6.SP.1.1 Compute the range, mean, median, and mode of data sets.
5.SP.1.2 Organize and display singlevariable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.
7.SP.1.1 Know various forms of display for data sets, including a stemandleaf plot or boxandwhisker plot; use the forms to display a single set of data or to compare two sets of data.
Definitions:
Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P ( A  B ), and is read "the probability of A , given B ".
Joint probability is the probability of two events in conjunction. That is, it is the probability of both events together. The joint probability of A and B is written P(A \cap B) or P(A,B) .

NS
 Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers
Exhibit knowledge of logarithms and geometric sequences
Apply properties of complex numbers


EE
 Write expressions that require planning and/or manipulating to accurately model a situation
Write equations and inequalities that require planning, manipulating, and/or solving
Solve simple absolute value inequalities


GR
 Match number line graphs with solution sets of simple quadratic inequalities
Identify characteristics of graphs based on a set of conditions or on a general equation such as y=ax^2+c .
Solve problems integrating multiple algebraic and/or geometric concepts
Analyze and draw conclusions based on information from graphs in the coordinate plane


PF
 Draw conclusions based on a set of conditions
Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas
Use relationships among angles, arcs, and distances in a circle


ME
 Use scale factors to determine the magnitude of a size change
Compute the area of composite geometric figures when planning or visualization is required


FU
 Write an expression for the composite of two simple functions
Use trigonometric concepts and basic identities to solve problems
Exhibit knowledge of unit circle trigonometry
Match graphs of basic trigonometric functions with their equations

